It means "woman from Arles". Its use outside of French is most familiar in the name of a series of paintings done of by Van Gogh. In that case "L'Arlésienne" referred to a Madame Ginoux whom both Van Gogh and Gauguin painted as the particular woman from Arles.

Next most common as far as I can tell is its use in the name of a play by Alphonse Daudet titled simply "L'Arlésienne." The play and the events surrouding it seem to have significantly more cultural relevance and familiarity within France. Otherwise the name as referring to the music written for the play, composed by Bizet, eclipses actual awareness of the play itself at least as far as I can tell.

The less than glorious history of that play relates to its use as part of a particular French idiom "jouer l'arlésienne" which literally translates to "to play the girl from Arles." It's used to refer to something that fails to materialize, similar to the expression "vapor ware" in English. That's probably what they meant, they just said it in a way which almost guaranteed most non-french speakers would have no idea what they were saying. The only reason I knew is because someone tricked me into studying French for 9 years and it came up in a trivia game we played as a way to help study.